[/JJGHT] FEBRUARY 12, 1910
EFFECT OF THE WIND
ON FLIGHT SPEEDS. BY LOUIS TOFT, M.Sc.
THE problem relating to the motion of a flying body
relative to the earth, the velocity of the wind, and the
velocity of the body relative to the air being known,
seems to be presenting some difficulty to many people
interested in the science of aviation. The problem
becomes very much simplified when it is noticed that
the motion of a flying body consists of two portions, the
first being the motion which the body performs relative
to the air, and the second the motion which the body
has due to its being carried along with the air itself at
the same speed as, and in the direction of, the wind.
B VELOCITY OF WIIND
Suppose a body is flying through the air with its
direction of motion relative to the air along the line AB
(Fig. 1), and let AB represent to scale the speed of the
body relative to the air. Suppose, further, there is a
wind blowing, the speed and direction of which are
represented by BC. Then, obviously, if there were no
wind, the body would move from A to B in an hour.
If now the body were allowed to drift with the wind
Fig. 2 3-
A
Fig 3 c B
for a second hour it would move from B to C. As
both these motions take place together, the body, instead
of moving from A to B, and then on to C, would
actually move from A to C along the line AC. As
AC is therefore the actual length travelled in one hour,
it will represent to scale the real velocity of the body
both in magnitude and direction. The rule for finding
the real velocity of a flying body may consequently be
stated as follows. Draw AB to represent to scale the
velocity of the body relative. to the air. Draw BC to
represent the velocity of the wind. Join A to C, and
AC will represent the real velocity of the body.
If the body is moving in the same direction as the
wind, AB and BC are in the same straight line, so that
the length AC will be the sum of the lengths of AB and
BC (Fig. 2), consequently the real speed will be the
arithmetical sum of the speed of the body relative to the
air and the speed of the wind. It is clear also, that if
the body is moving directly against the wind, the real
speed will be the arithmetical difference between the
speed of the body and the speed of the wind (Fig. 3).
Now examine one or two cases of flights in the wind.
(1) An out-and-home flight of 60 miles each way, with
a wind blowing outwards along the course. Let the
velocity of flight relative to the air be 40 miles an hour,
and the velocity of the wind 20 miles an hour. The real
velocity on the outward journey is 40 + 20 = 60 miles
an hour, and that on the return journey is 40- 20 = 20
miles an hour. The time taken for the double journey will
be -y—I = 4 hours, as compared with — = 3 hours
60 20 r 40 J
in still air.
(2) A flight 60 miles out-and-home with a side wind.
The velocity diagram for this case is shown in Fig. 4.
By measurement, or by cal
culation, AC is found to
represent a velocity of 34*6
miles per hour. The real
velocity on the return
journey will also be 34^6
miles per hour, so that the
time taken for the double 120
journey will be —.> = 3*47
hours, as compared with 3
hours in still air.
(3) An out-and-home flight of 60 miles each way, with
a wind blowing at 6o° with the direction of the course.
The velocity diagram for the outward motion is given
in Fig. 5.
By measurement or by calculation, AC is found to
represent a velocity of 26 miles per hour.
108